Combine the coffee, sugar, coffee liqueur and vanilla and stir until the sugar dissolves. Pour the mixture into a 9-by-13-inch pan. Place the pan in the freezer for 1 hour, until the mixture starts to become slushy around the edges. Rake the mixture with a dinner fork to break up the crystals and place the pan back in the freezer. Every 30 minutes, rake the mixture, until it is completely frozen and granular throughout. Wrap well and keep frozen for a few hours, until ready to serve.
Spoon the granita into bowls or stemmed glasses, such as martini glasses, and top with a dollop of whipped cream. Serve immediately.